Relating The Standard And Factored Forms Worksheet - Chapter 3.2 (Page 3 of 11) in pdf

Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 3

Rachel’s revenue function is in

If you expand and simplify it to

factored form.

factored form

express it in

then you can compare both functions to see if they

standard form,

a quadratic function in the form

f(x) 5 a(x 2 r) (x 2 s)

are the same.

standard form

a quadratic function in the form

Beth’s Solution: Comparing and Analyzing the Functions

f(x) 5 ax

1 bx 1 c

R(x) 5 (40 2 x) (10 1 x)

I multiplied the binomials and

collected like terms. Rachel’s revenue

R(x) 5 400 1 40x 2 10x 2 x

function in standard form is the same

R(x) 5 400 1 30x 2 x

as Andrew’s revenue function, but

the terms are in a different order.

R(x) 5 2x

1 30x 1 400

I rearranged my function to match

Andrew’s.

0 5 2x

1 30x 1 400

zeros of a relation

The x-intercepts, or zeros, occur

0 5 (40 2 x) (10 1 x)

R(x) 5 0.

when the revenue is 0, so

the values of x for which a

relation has the value zero. The

I used Rachel’s function to find the

40 2 x 5 0

10 1 x 5 0

and

zeros of a relation correspond to

x-intercepts by setting each factor

40 5 0 1 x

x 5 0 2 10

the x-intercepts of its graph

and

equal to zero and solving for x.

40 5 x

x 5 210

and

The maximum value is the

(40 1 (210) )

y-coordinate of the vertex, and the

x 5

vertex lies on the axis of symmetry.

To find the axis of symmetry, I added

x 5

the zeros and divided by 2.

x 5 15

To find the maximum revenue

R(15) 5 (40 2 15) (10 1 15)

I substituted the x-value into

Rachel’s equation.

R(15) 5 (25) (25)

R(15) 5 625

The maximum revenue is $625.

134

Chapter 3

NEL

Relating The Standard And Factored Forms Worksheet - Chapter 3.2 Page 3

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